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Rearrangements and Majorization

  • Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

Many inequalities are known that involve real vectors and vectors with the components rearranged. Such inequalities are discussed in Chapter X of Hardy, Littlewood, and Pólya (1934, 1952), but a number of new results have been obtained since that book was written. Particularly 4 noteworthy is the work of Lorentz (1953) and Day (1972).

Keywords

Convex Function Convex Cone Notational Convenience Permutation Matrice Permutation Invariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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